High School Understanding Polar and Cartesian Graphs: Comparing Two Coordinate Systems

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The discussion clarifies that trigonometric functions can be graphed in both Cartesian and Polar coordinate systems, represented by (x,y) and (r,θ) respectively. The attached image demonstrates that both graphs depict the same function, confirming their equivalence when converting between coordinate systems. Participants express that while the concepts are clear, polar coordinates can be confusing for beginners. The conversation indicates a willingness to explore further questions about polar coordinates in the future. Understanding these two systems is essential for grasping trigonometric functions effectively.
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Please see the attached image.
To my understanding, there are two ways to graph a trigonometric function.
One is in the Cartesian Coordinate Plane where we have the values (x,y).
The other is in the Polar Coordinate system where we have the values (r,θ).

In regards to the image that I've attached, are these graphs saying the same thing, just in different coordinate systems?
 

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    Screen Shot 2018-06-29 at 1.51.05 PM.png
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Yes, both the graphs are representing the same function and have the same values if you will convert the coordinate system.
 
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Great thank you.
 
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Your welcome. Anyway, polar coords are confusing
 
Just starting learning about them, so I'm sure I'll have questions later.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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